In previous work it was shown that progress in attaining and maintaining stable mean reversed-field pinch (RFP) profiles can be made by abandoning the steady-state assumption and instead seeking solutions of the pressureless (force-free), one-dimensional transport equations that are separable in time and space [E. J. Caramana and R. A. Nebel, Phys. Fluids 31, 3322 (1988)]. Here these solutions have been extended to two dimensions and therefore the previous formalism is also applicable to toroidal and helical states as well as axisymmetric cylindrical states. Furthermore, the one-dimensional separable solutions are demonstrated to be three-dimensional attractors, provided that the separable profiles are stable to current-driven modes. The sensitivity of these states to the velocity boundary conditions and to dimensionless parameters such as the Lundquist number and the magnetic Prandtl number has been studied. The stability boundary between one-dimensional stable solutions and unstable rampdown solutions has also been explored. Simulations with finite pressure and self-consistent transport clearly show the improved confinement that can be achieved with plasma rampdown. Finally, reactor simulations demonstrate that self-similar tearing mode stable rampdown discharges can lead to pulsed systems that show significant net energy gain.
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Nebel et al. (2002) studied this question.